Download Ricardian Equivalence

Economic Modelling
Ricardian Equivalence: Example of Two Period
General Equilibirum with Taxes with Representative
Agents
Dr. Keshab Bahttarai,
Business School University of Hull
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Ricardian Equivalence: Main Proposition
• How important is a tax cut?
• Should government finance deficit by
borrowing or by raising taxes?
• Ricardian Equivalence Theorem is after
David Ricardo.
• British economist, who wrote about 180 years
ago that it does not matter whether
government finances its deficit by
– borrowing or
– taxes.
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Ricardian Equivalence: Main Proposition
• If it borrows now it raises tax in future for repayment
of its debt.
• With more current debt private households save
more in anticipation of higher taxes in the future that
government will impose on them to repay the debt.
• Private households optimise intertemporally and
completely internalise public policy.
• Borrowing only or tax only strategy does not matter if
both the government and household honour their own
inter temporal budget constraints.
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Basic Proposition of the Ricardian Equivalence
Tax or Borrowing Does not Make Any
Difference
Tomorrow C2
Before Borrowing
Budget Constraint
After borrowing
budget constraint
C1 +
C1 +
C2
=
1+ r
(w 1 ) +
⎛ w2 ⎞
⎜
⎟
⎝1+ r ⎠
τ ⎞
C2
⎛ w
= (w1 − τ 1 ) + ⎜ 2 − 2 ⎟
1+ r
⎝1+ r 1+ r ⎠
C1
Today
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Model Economy for Ricardian Equivalence Theorem
Preference of households:
U (C 1 , C 2 ) = ln C 1 + β ln C 2
Endowments:
Government policy:
{w 1 , w 2 }
{G 1 , G 2 , τ 1 , τ 2 , B }
Budget constraint for N identical households (in real
terms)
C 1 + b ≤ w1 − τ 1
Period 1:
C 2 ≤ b (1 + r ) − τ 2
Period 2:
Budget constraint for the Government:
Period 1:
Period 2:
G1 + B ≤ N τ 1
G 2 ≤ B (1 + r ) + N τ 2
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Tax Spending and Borrowing Strategies
Inter-temporal budget constraint for the government:
G2
Nτ 2
G1 +
= Nτ 1 +
1+ r
1+ r
Two strategies of financing fixed amount of
(i)
G1 and G2
Taxes only strategy: {G1 , G2 ,τ 1 ,τ 2 , B = 0}
{
}
(ii) Borrowing strategy G1 , G 2 ,τ 1 = 0,τ 2 , B
Market clearing for goods in period 1 and 2:
NC1 + G1 = Nw1
NC2 + G2 = Nw2
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Optimisation for Ricardian Equivalence Theorem
Inter temporal budget constraint for individuals
T2 ⎞
C2
⎛ w2
= (w1 − T1 ) + ⎜
−
C1 +
⎟
1+ r
⎝1+ r 1+ r ⎠
(2)
where T1 = N τ 1 T2 = N τ 2
⎡ C2
⎛ W2 T2 ⎞⎤
L = ln C1 + β ln C2 + λ C1 +
⎢ 1 + r − (W1 − T1) − ⎜1 + r − 1 + r ⎟⎥
⎝
⎠⎦
⎣
First order condition for optimisation:
C2 1
= 1 + r =>
β C1
C 2 = β (1 + r )C1
Using it in the intertemporal budget constraint:
1 ⎡
⎛ W2
(W1 − T1 ) + ⎜
C1 =
⎢
1+ β ⎣
⎝1+ r
⎞⎤
−
⎟⎥
1 + r ⎠⎦
T2
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Conclusion of the Ricardian Equivalence Theorem
Given that number of households remains N
The strategy 1 gives solution to consumption as above.
There is no borrowing but only taxes in both periods.
*
*
c
c
=
w
−
g
Per Capita Consumption 1
1
1 ; 2 = w2 − g 2 .
In strategy 2 government cuts taxes to 0 in the first
period and borrows to finance services and pays back by
paying higher taxes in period 2.
These two financing scheme are equivalent. Because if
government borrows 1 now, it has to pay back (1 + r ) in
period 2. Tax also has to increase by (1 + r ) in period 2.
People anticipate higher taxes in future and save more in
period 1 to be able to pay in period 2.
These two effects offset each other.Both strategies of
financing public deficit yields the same result.
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Numerical Proof of Ricardian Equivalence Theorem -1
Tax only Strategy
{w1 , w2 } = {100,100}
Endowments:
Interest rate
5%
Lump Sum Taxes in periods 1 and 2
τ 1 = 20 ; τ 2 = 20
Thus the government is committed to provide services
⎛ 100 ⎞
R = 0.2(100 ) + 0.2⎜
⎟ = 39.04
1
.
05
⎝
⎠
Using these information in consumption function for
period
1 ⎡
80 ⎤
⎛ W2 T2 ⎞⎤ 1 ⎡
(W1 − T1 ) + ⎜ − ⎟⎥ = ⎢80 +
C1 =
⎢
1+ β ⎣
1.05 ⎥⎦ =82.2
⎝ 1 + r 1 + r ⎠ ⎦ 1 .9 ⎣
Consumption in period 2
C 2 = β (1 + r )C1 = 0.9(1.05)(82.2) = 77.8
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Borrowing strategy: period 1 borrowing of 30
T2 = ?
if
T1 = 0
(it will certainly be higher)
Fix the consumption level as before at
T2
1 ⎡
⎛ 100
⎞⎤
+
−
100
C1 =
⎜
⎟⎥
1 + 0 .9 ⎢⎣
1
+
0
.
05
1
+
0
.
05
⎝
⎠⎦
1 ⎡
⎛ 100
+
82 .2 =
100
⎜
1 + 0 .9 ⎢⎣
⎝ 1 + 0.05
−
c1 = 82.2
⎞⎤
⎟⎥
1 + 0 .05 ⎠ ⎦
T2
⎡
100 ⎫⎤
⎧
T2 = ⎢1.05 ⎨(82 .2 × 1.9 ) − 100 −
⎬⎥ = 41 .1
1.05 ⎭⎦
⎩
⎣
Thus taxes in period 2 has risen to 41.1.
Loan repayment B (1 + r ) = 30 (1 .05 ) = 31.5;
c 2 = β (1 + r )c1 = 0 .9 (1 .05 )82 .2 = 77.68
Since households know that they have to pay so much of
taxes in period 2, they increase their saving in period 1 in
anticipation of higher taxes in period 2.
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Limitations of Ricardian Equivalence Theorem
Why was there a big concern on accumulation of public debt in 1970 and
early 1980s? Also to debt accumulation in many developing economies?
By Ricardian Equivalence private saving rises against an increase in the
public sector deficit.
If private sector saving compensates for public sector deficit then there is
no alteration in national saving in response to public debt.
There is no crowding out between public and private sector.
This does not hold when private agents face inter generational borrowinglending constraint or if it takes long time for government to increase taxes
to repay debt.
By choosing deficit financing by borrowing government is promoting
inter generational transfers because current debts may be paid by taxing
people in the far distant future generation.
Main issue in this intergenerational transfer is that how many people save
for their children, grand children or grand-grand children?
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How Big the Debt Problem Around the World?
Debt Outstanding and Debt Services (in Billion of US $)
2002
1990
Debt
Debt
Debt
Debt
Service
Service
DEVELOPING COUNTRIES
2186.4
315.2
1259.8
140.6
AFRICA
268
26.9
244.3
16.9
SUB-SAHARA AFRICA
221.3
18.4
187.6
13.5
DEVELOPING ASIA
711.1
89.9
335.5
36
MIDDLE EAST
426
44.3
234.7
24.1
WESTERN HEMISPHERE
781.3
154.2
445.2
63.5
COUNTRIES IN TRANSITION
374.7
51.6
203.2
44.1
CENTRAL AND EASTERN
195.6
31.8
113.6
25.7
EUROPE
COMMONWEALTH OF
179.1
19.9
89.6
18.4
INDEPENDENT STATES AND
MONGOLIA
COMMONWEALTH OF
46.2
5.2
0.1
0.1
INDEPENDENT STATES AND
MONGOLIA, EXCL RUSSIA
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References
•
Barro, R. J. (1974), "Are Government Bonds Net Wealth?," Journal
of Political Economy pp. 1095-1117.
•
Clark Tom , M Elsby and S Love (2001) Twenty Five Years of Falling
Investment? Trends in Capital Spending on Public Services, Institute of
Fiscal Studies.
HM Treasury (2002) Reforming Britain’s Economic and Financial Policy,
Palgrave, Institute for Fiscal Studies (2002), The IFS Green Budget,
January.
•
•
Ricardo David, Principles of Political Economy
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